Q. 36 I5.0( 1 Vote )

Find one-paramete

Answer :


Given







This is a first order linear differential equation of the form



Here, P = sec2x and Q = tan x sec2x


The integrating factor (I.F) of this differential equation is,



We have


I.F = etan x


Hence, the solution of the differential equation is,





Let tan x = t


sec2xdx = dt [Differentiating both sides]


By substituting this in the above integral, we get




Recall





yet = tet – et + c


yet × e–t = (tet – et + c)e–t


y = t – 1 + ce–t


y = tan x – 1 + ce–tan x [ t = tan x]


Thus, the solution of the given differential equation is y = tan x – 1 + ce–tan x


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